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\author{JESOP Bernard}
\title{ Adaptation of ANDy to metabolic network representation }
\begin{document}
\maketitle
\newpage
%TODO I didn't talk about co-factor, detailed the reactions etc...
%TODO talk about complex regulation of the network

% Goals %
% We want to explicite how we can answer question with Randy
% For example, at the metabolic level, Can randy give answer that FBA already answer in a more efficient way
% It will be hard to use Randy for answering quantitative model.
% because FBA is already well installed and very efficient

% We already know that randy can fit regulatory network, and give some analysis


\section{Introduction}

%\cite{gutenkunst_universally_2007}


%The word "metabolism" is derived from the greek {$\mu\varepsilon\tau\alpha\beta o \lambda\'\eta$ }\\
%\textgreek{metabol}

The cellular metabolism is the network of reaction in which nutrients are broken down to make energy plus primary metabolites; in which all the components of the cell are synthesized. The intermediate and final products of metabolic reactions are called metabolites. \\

Reactions that break down sources of energy and materials are called catabolic [fig \ref{fig:ana_cata}]. For instance, \textit{glycosis} starts from a glucose molecule and break it down into pyruvate, a key metabolite in \textit{Citric Acid Cycle}. From an energetic point of view, this degradation will produce 2 ATP molecules and 2 NADH molecules from one glucose molecule.  In further details, this degradation, from glucose to pyruvate, is about 10 successive reactions. That succession of reaction is very common in the cell, they are called \textit{pathways}. Pathways are the smallest functional entities of a metabolick network.	\\


 Since, in the living conditions, most of the cell reactions are either impossible or very slow, most of the chemical reactions have to be catalysed by proteins called \textit{enzymes}. Proteins are a linear chain of amino acids with a specific structure such that they can favour a particular reaction.\\
Reactions that synthesize components are called anabolic [fig \ref{fig:ana_cata}]. Intuitively, all the pathway leading to a synthesis are anabolic, they will need to consume energy to occur. Typical exemples of pathways in the anabolism are amino acids synthesis, nucleic acids synthesis or fatty acid synthesis.\\

\begin{figure}[here]
\includegraphics[scale=0.2]{figures/anabolism_catabolism.jpg}
\caption{"caption"}
\label{fig:ana_cata}
\end{figure} 
% The structure of metabolic networks varies between species, however some similarity remains between them.
Our knowledge on species metabolic network does not stop growing. The first metabolic networks have been constructed by cutting all the known metabolic pathways of a species to a set of biochemical reactions. \\
Now, thanks to high-throughput technology and big data analysis, we are able to automatically reconstruct the metabolic network of a species from its annotated genome. However, the resulted metabolic network, called \textit{draft} metabolic network, have still to be manually curated by experts. Build a fully effective metabolic network is not an easy task. Many databases like KEGG, metaTIGER or MetaCyc gathered a huge amount of data on metabolic pathways, for instance KEGG gather up to 3000 metabolic networks of prokaryotes and eukaryotes [].\\

%TODO Why do we study metabolism? Variation in homeostasis can create disease. 
%Moreover, 


%Then, using a graph representation, you can link reactants to product, where the link represent the specific enzymatic reaction. This kind of representation have been a breakthrough in biology, allowing an holistic view of the organism. \\


%called \textit{catabolism}(e.g. ATP NADH)
%called \textit{analolism} (e.g. nucleotides, nucleosides, amino acids, lipids, etc)

%The metabolism is the entire set of chemical reactions used to maintain the cells alive. 
%This set of reactions can be conceptually separated into two categories: catabolism or the degradation of nutrients to generate energy and starting materials; and anabolism or the synthesis of all compounds required by the cells like DNA, RNA and protein synthesis.
The study of metabolic network is very important in order to study some ...

In the Big Data area, there is a crucial need of analytic method to extract knowledge on metabolism. A large variety of mathematical tools have try to model metabolic network (e.g differential equations, boolean network, flux balance analysis, cellular automata, petri nets). However, they all have their limitations.\\
In this work, we aim to introduce a new framework to represent metabolic network using the petri net with causal time ANDy. Firstly, we will present previous modelling concepts. Secondly, we will present ANDy formalism. Finally, we will introduce metabANDy,and how to model metabolism with ANDy. 


\section{Modelling metabolism}
%One can compare a cell to a micro-factory, where a bench of chemicals usally called metabolites, are transformed in order to produce the needed co the cell alive. Those transformations are chemicals reactions, they are very often catalysed by enzymes.
Metabolic network are typically represented as graphs, where the metabolites are the nodes and the link are the enzymatic reactions. This representation is not so easy because reactions often involve many reactants and products, making the network rapidly incomprehensible for human, see [fig \ref{fig:metabo_net}]. 

A metabolic network can be analyse from a topological point of view, or a dynamical point of view. In the former, one would like to understand what are the variation in the topology associated with a disease, for exemple. This can be done with a boolean network referring to the presence of abscence of metabolites. In the later, one would like to study the system in a quantitative manner. How does the metabolite concentration evole over the time? This require to specify enzyme kinetics of the reactions.  \\

%A metabolic network is the set of biochemical reactions occuring in the cell. It have been modelled with various mathematical tools. We will first present those existing tools, how they have been used, their advantages but also their limitations. We will then introduce how we propose to model metabolism in ANDY.

%Most of the time, those reactions are catalysed by enzymes and help to sustained the requiments of the cells. 

%
%We can represent the metabolism of an organism using graphs, where the nodes are metabolites, and the vertices are the enzymatic activity. Notice that many enzymes can have the same enzymatic activity. 
%
%Some databases ,like KEGG, metaCyc, or BRENDA, gathered those metabolic networks and give additional information on the specific enzyme kinetics in different organisms, for example.

\begin{figure}[here]
\begin{center}
\includegraphics[scale=0.06]{figures/KEGG-Intermediary-Metabolism.png}
\caption{\textbf{Overview of a metabolic representation in KEGG}}
\label{fig:metabo_net}
\end{center}
\end{figure}

\subsection{Time modelling}
Time representation in metabolic model have mainly been study using differential equation models. By representing reaction kinetics with michaelis-menten equation, they allow, to analys in a quantitative manner the concentration variation of the molecule over the time in small metabolic systems. Howver, when they are applied to larger systems, they become extremely large to analyse. 
\subsubsection{Enzyme kinetics}

%In metabolism modelling it is essential to know the rates with which enzymes catalyse the reactions. 
%In a metabolic network, there is a lot of chemical reactions between the metabolites. Most of them are catalysed by enzymes. The kinetics of those interaction help us to study the dynamics of the system. 
The \textit{rates} with which enzymes catalyse the reaction is essential in dynamical study. 
\subsection{Space modelling}
\subsubsection{Compartments}

\section{ANDy}


\section{Proposition}

\bibliographystyle{plain}
\bibliography{ANDY.bib}

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